CN109687467A - A kind of power grid Interval Power Flow improved method considering interval connection - Google Patents

A kind of power grid Interval Power Flow improved method considering interval connection Download PDF

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CN109687467A
CN109687467A CN201910125928.5A CN201910125928A CN109687467A CN 109687467 A CN109687467 A CN 109687467A CN 201910125928 A CN201910125928 A CN 201910125928A CN 109687467 A CN109687467 A CN 109687467A
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power
node
interval
correlation
branch
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CN109687467B (en
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冷仕鹏
冉晓洪
刘开培
陈书瑶
张珣玥
李思伟
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Wuhan University WHU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention belongs to electric system Interval Power Flow computing technique field more particularly to a kind of power grid Interval Power Flow improved methods for considering interval connection, including input electric power system parameter；Interval Power Flow is converted into nonlinear optimal problem using affine arithmetic；Choose n-th pair of generator output variable with correlationX i 、X j ；Establish the parallelogram model between correlated variables；By parallelogram model conversation at the inequality constraints condition of analytical form；N=n+1 is enabled, if judgement n >=N, carries out next step, otherwise return to previous step；The constraint of simultaneous power flow equation and correlation constraint, with nonlinear optimization algorithm solution interval trend.This method considers the correlation in electric system between variable, and uncertain Load flow calculation can be made more accurate, provides more accurately reference to electric power system dispatching.

Description

A kind of power grid Interval Power Flow improved method considering interval connection
Technical field
The invention belongs to electric system Interval Power Flow computing technique field more particularly to a kind of power grids for considering interval connection Interval Power Flow improved method.
Background technique
In practical power systems operational process, either all there is constantly fluctuated for load or node injecting power Situation, these have resulted in the uncertainty of electric power system tide calculating, have proposed challenge to the scheduling planning of power grid.For not The treating method of certain problem, at present for be generally divided into three kinds of random theory, fuzzy set theory and interval analysis methods.Its In the probability density function or membership function of uncertain parameter required no knowledge about due to interval analysis, calculating process is easy, so Interval analysis at present is widely used in uncertain Load flow calculation.Initial Interval Power Flow operation exactly brings interval number into tide Flow equation, and interval iteration is carried out using Krawczyk-Moore operator, Interval Power Flow result is obtained with this.But this method pair Very stringent in the selection requirement of initial value, inappropriate initial value easilys lead to result and does not restrain；Simultaneously because interval algorithm sheet The conservative of body is likely to expand calculated result in an iterative process, it is invalid to even result in compartmental results.
Therefore in the calculating of current electric system Interval Power Flow, common method is effectively to inhibit section using affine arithmetic The expansion of arithmetic, and nonlinear optimal problem is converted by interval iteration.Nonlinear optimization can use general Mathematical Planning Model indicates, that is, gives an objective function, and one group of solution is found under constraint condition and makes objective function maximum or minimum, tool The mathematical form of body is expressed as follows:
Wherein x indicates that variable, f (x) indicate the objective function about x, the minimum value of f (x) in min f (x) representative function； gi(x)≤0 i-th of inequality constraints about x is indicated, p indicates the number of inequality constraints；hi(x)=0 indicate i-th about The equality constraint of x, q indicate the number of equality constraint.
In the Interval Power Flow based on affine arithmetic calculates, objective function is generally node voltage amplitude, node voltage phase Angle, branch active power and branch reactive power, and constraint condition is then determined by Load flow calculation formula.Nonlinear optimization is asked Topic, it is however generally that, constraint condition is stronger, and resulting solution also can be more accurate.
In the power system, the active power and reactive power of different node injections might not be all independent from each other, Such as in wind power plant adjacent blower power output situation, since wake effect may there is certain correlations between them. And currently based in affine Interval Power Flow calculating, constraint condition only considered general electric system rule, and ignore Correlation that may be present between variable, can virtually amplify the feasible zone of nonlinear optimization in this way, may cause the deviation of solution.
Correlation between interval variable is a kind of non-deterministic relation of interdependence existing for a kind of objective phenomenon, i.e., from Each value of variable, dependent variable are non-deterministic with the numerical value corresponding to it due to being influenced by enchancement factor.It is counting On, the correlativity of two variables can analytically be indicated with related coefficient, can also be intuitively with scatter plot in coordinate diagram Middle expression.
Summary of the invention
The object of the present invention is to provide a kind of correlations by between interval variable to be indicated with parallelogram model, and is utilized Correlativity is converted into inequality constraints condition and is applied to the method that the Interval Power Flow based on affine arithmetic calculates by the model.
To achieve the above object, the technical solution adopted by the present invention is that: it is a kind of consider interval connection power grid section tide Flow improved method, comprising the following steps:
Step 1, input electric power system parameter node load consume power, node generator injecting power, reference voltage, base Quasi- power, branch impedance, injecting power fluctuation range, the node serial number with correlation and sexual intercourse book size；
Interval Power Flow is converted to nonlinear optimal problem using affine arithmetic by step 2；If undulate quantity is node injection Active-power P and reactive power Q, the noise size that they generate node areWithThe initial value of noise is [- 1,1]； Voltage real part eiWith voltage imaginary part fiIt is expressed as follows with the linear combination about noise:
Wherein nP indicates the set of PQ node and PV node；The set of nQ expression PQ node；ei,0、fi,0Respectively indicate i section Point voltage magnitude real part eiWith imaginary part fiThe central value of affine form；It respectively indicates since j node injects active power Fluctuation causes ei、fiDeviation；E Biao Shi not be caused since j node injects reactive power fluctuationi、fiDeviation；
Wherein objective function are as follows:
Node voltage amplitude
Node voltage phase angle
Branch active power
Branch reactive power
Wherein Pij、QijRespectively indicate the active power and reactive power of branch between node i and node j；Gij、BijRespectively Indicate the i-th row jth column element value in the real-part matrix and imaginary-part matrix of grid nodes admittance matrix；
Constraint condition expression formula are as follows:
Wherein, XiFor noiseWithLinear combination；DiIndicate XiBound section；Inf indicates interval limit, sup Indicate the section upper limit；
Step 3 sets and has N to contribute variable the distributed generation resource with correlation in power grid, chooses wherein n-th pair of correlation Power output variable XiAnd XjIt is sampled, the parallelogram model between correlated variables is established, by parallelogram model conversation at solution The inequality constraints condition of analysis form:
Wherein ktFor constant, specific value is the slope k of parallelogram model four edges1、k2；
Step 4 enables n=n+1, if n >=N, carries out step 5, otherwise return step 3；
Step 5, with step 2 Chinese style (2), (3), (4), (5) be objective function, step 3 Chinese style (14) be constraint condition pair Power grid Interval Power Flow is solved；
Step 6, the solution for exporting power grid Interval Power Flow: node voltage amplitude bound, node voltage phase angle bound, branch Active power bound and branch reactive power bound.
Beneficial effects of the present invention: general based in affine Interval Power Flow computational problem, the constraint condition of variable The feasible zone of objective function solution is constituted, the change of feasible zone largely will lead to the change of optimal solution.And Interval Power Flow In constraint condition generally only considered electric system objective power flow equation limitation content, do not account for generator injecting power Correlativity between equal variables.Correlativity between interval variable is converted into inequality constraints and is added thereto by the present invention, Constraint condition can be enhanced, reduce feasible zone, obtain more accurate optimal solution.Method of the invention considers in electric system Correlation between variable can make uncertain Load flow calculation more accurate, provide more accurately ginseng to electric power system dispatching It examines.
Detailed description of the invention
General parallelogram model of the Fig. 1 between two interval variable of one embodiment of the invention；
Fig. 2 is the geometrical relationship figure of one embodiment of the invention interval variable correlation and constraint condition；
Fig. 3 is the flow chart of one embodiment of the invention；
Fig. 4 (a) is that one embodiment of the invention is applied to IEEE9 voltage magnitude example figure, and Fig. 4 (b) is the present invention one Embodiment is applied to IEEE9 voltage phase angle example figure, and Fig. 4 (c) is that one embodiment of the invention is applied to IEEE9 branch wattful power Rate example figure, Fig. 4 (d) are that one embodiment of the invention is applied to IEEE9 branch reactive power example figure.
Specific embodiment
Embodiments of the present invention are described in detail with reference to the accompanying drawing.
The present embodiment enhances the constraint condition of nonlinear optimal problem using the correlativity of variable, in this, as improvement side Case simultaneously proposes a kind of new solution, so that the interval solutions that power grid Interval Power Flow calculates is more accurate.
The present embodiment is achieved through the following technical solutions, a kind of Interval Power Flow improvement side considering interval connection Method, implementation step are as follows:
Step 1: input electric power system parameter, mainly include node load consumption power, node generator injecting power, Reference voltage, reference power, branch impedance, injecting power fluctuation range, the node serial number with correlation and sexual intercourse book are big It is small；
Step 2: Interval Power Flow is converted to nonlinear optimal problem with affine arithmetic.It is assumed that undulate quantity is node note The active-power P and reactive power Q entered, the noise size that they generate node areWithThe initial value of noise be [- 1,1].Fundamental quantity in this way in Load flow calculation, voltage real part eiWith voltage imaginary part fiThe linear combination table about noise can be used Show as follows:
All variables can be by e in Load flow calculationiAnd fiIt is calculated, so all variables all available noisesWithIt indicates.
Wherein objective function is node voltage amplitude, node voltage phase angle, branch active power and branch reactive power, table Show that mode is as follows:
I. node voltage amplitude
II. node voltage phase angle
III. branch active power
IV. branch reactive power
Constraint condition is according to the available following expression-form of Load flow calculation equation:
Wherein XiIt is also noiseWithLinear combination.
Step 3: assuming have N to the distributed generation resource power output variable with correlation in power grid, wherein n-th pair of change is chosen Amount, makes scatter plot according to the sampled value of the two power output, and depict the parallelogram model of two variables.Then it will put down Row quadrangle model conversation at analytical form inequality constraints condition.
3.1, two variables of selection are sampled, and sampled value is depicted as scatter plot；
3.2, with a parallelogram envelope-sampling point, wherein envelope-sampling point is most and the smallest parallel four side of area Shape is most suitable；
3.3, according to established parallelogram model, calculate the related coefficient size between two variables.It is assumed that I-th and j-th of variable XiAnd XjBetween have correlation, concrete model description as shown in Fig. 1, in figure,Indicate that section becomes Measure XiSection radius, Indicate XiSection central value,The phase between two variables can be calculated according to the half diagonal of parallelogram long a, b Coefficient magnitude is closed, formula of correlation coefficient is defined as follows
3.4, according to parallelogram model foundation concrete analytical expressions.Parallelogram model analyzing expression formula is such as Under:
|ρ-1T-1R-1(X-XC) |=| C-1(X-XC)|≤e (8)
Wherein | | indicate the absolute value of each element in vector, the definition difference of matrix ρ, T, R, e are as follows:
E=[1 1]T.
According to above-mentioned mathematical model, two interval variables with correlation can be converted into two independent variables δi、δj (δi,δj=[- 1,1]) linear combination.Expression is as follows:
X=RT ρ δ+XC (9)
Namely
3.5, X is setiAnd XjBetween reasonable relational expression, make its envelope parallelogram model.The purpose of this step It is for the correlation between interval variable to be converted into new constraint condition.
(1) when not considering interval variable correlation
When only considering power flow equation constraint, about variable XiAnd XjConstraint condition condition be
It is presented as that outer profile is the rectangle ABCD of dotted line in fig. 1, can be regarded as by Xi、XjWhat two variables formed Feasible zone.But its actual feasible zone only has the parallelogram-shaped segment AECF in attached drawing 2, so not considering correlation Shi Huiwu Amplify feasible zone in shape, causes the inaccurate of solution.
For parallelogram model, newly-increased constraint expression form is
inf(kDi+Dj)≤kXi+Xj≤sup(kDi+Dj) (12)
But when not considering correlation actually, the newly-increased constraint and formula (11) are of equal value, not by whole constraint enhancing, just Such as dotted line L1, the L2 newly increased in attached drawing 2, feasible zone is not reduced.
(2) when considering interval variable correlation
Considering XiAnd XjBetween correlation after, according to step 3.4 calculate kXi+XjIt can obtain more accurate upper and lower Boundary, it is as follows
inf(Dij)≤kXi+Xj≤sup(Dij) (13)
Its result has inf (Dij) > inf (kDi+Dj), sup (Dij) < sup (kDi+Dj), in this way, newly-increased pact Beam enables to whole constraint condition to be enhanced.Solid line L3, L4 are shown as in fig 2, accurately approach parallel four side Shape can reach the effect of feasible zone envelope parallelogram.
To sum up, after considering the correlations of variables such as generator output, constraint condition becomes:
Step 4: considering the correlation between the interval variables such as other generator outputs, return step according to the actual situation Three carry out the conversion of correlation to constraint condition again, and enable n=n+1, until all correlation of variables have considered, i.e. n= N。
Step 5: in step 2 formula (2), (3), (4) (5) for objective function, the formula (14) in step 3.5 is constraint Condition optimizes problem solving.Wherein node voltage amplitude, branch be active and branch it is idle be quadratic function, two can be used Secondary planning is solved, and node voltage phase angle is general nonlinearity function, is solved using nonlinear optimization method.
The solution of general optimization problem is the minimum value that objective function can be got in constraint condition, so for Interval Power Flow For solution, first according to target function f (x) acquires lower bound of the minimum value a as interval solutions, then objective function is negated acquire it is negative Minimum value-the b of objective function-f (x), this minimum value is negated again be exactly former objective function maximum value b, as interval solutions The upper bound, i.e. interval solutions are [a, b].
Step 6: output considers the solution of the power grid Interval Power Flow of interval connection, including node voltage amplitude bound, section Point voltage phase angle bound, branch active power bound and branch reactive power bound.
The process that the present embodiment is realized is as shown in Figure 3.
When the present embodiment is applied to IEEE9 power transmission network, connect respectively in 6, No. 8 nodes of 9 node system of standard IEEE first Enter power be 0.6MW and 0.8MW wind-driven generator, it is then assumed that in IEEE9 power transmission network the injection active power of 4-9 node and Reactive power has uncertainty, and fluctuation range is ± 10%；Consider that 6, No. 8 nodes access wind-driven generator active power Correlation, and related coefficient be -0.4；Simultaneously to consider the Monte-carlo Simulation Method calculated result of correlation as exact value It compares, Monte Carlo frequency in sampling is 10,000 time.It emulates to obtain using Matlab and considers that correlation is related to not considering Property comparison of computational results See Figure, Fig. 4 (a) is applied to IEEE9 voltage magnitude example figure, and Fig. 4 (b) is that should be used for IEEE9 Voltage phase angle example figure, Fig. 4 (c) are that should be used for IEEE9 branch active power example figure, and Fig. 4 (d) is applied to IEEE9 branch Road reactive power example figure.
It should be understood that the part that this specification does not elaborate belongs to the prior art.
Although being described in conjunction with the accompanying a specific embodiment of the invention above, those of ordinary skill in the art should Understand, these are merely examples, various deformation or modification can be made to these embodiments, without departing from original of the invention Reason and essence.The scope of the present invention is only limited by the claims that follow.

Claims (1)

1. a kind of power grid Interval Power Flow improved method for considering interval connection, characterized in that the following steps are included:
Step 1, input electric power system parameter node load consume power, node generator injecting power, reference voltage, benchmark function Rate, branch impedance, injecting power fluctuation range, the node serial number with correlation and sexual intercourse book size；
Interval Power Flow is converted to nonlinear optimal problem using affine arithmetic by step 2；If undulate quantity is the active of node injection Power P and reactive power Q, the noise size that they generate node areWithThe initial value of noise is [- 1,1]；Voltage Real part eiWith voltage imaginary part fiIt is expressed as follows with the linear combination about noise:
Wherein nP indicates the set of PQ node and PV node；The set of nQ expression PQ node；ei,0、fi,0Respectively indicate i-node electricity Pressure amplitude value real part eiWith imaginary part fiThe central value of affine form；It respectively indicates since j node injects active power fluctuation Cause ei、fiDeviation；E Biao Shi not be caused since j node injects reactive power fluctuationi、fiDeviation；
Wherein objective function are as follows:
Node voltage amplitude
Node voltage phase angle
Branch active power
Branch reactive power
Wherein Pij、QijRespectively indicate the active power and reactive power of branch between node i and node j；Gij、BijIt respectively indicates The i-th row jth column element value in the real-part matrix and imaginary-part matrix of grid nodes admittance matrix；
Constraint condition expression formula are as follows:
Wherein, XiFor noiseWithLinear combination；DiIndicate XiBound section；Inf indicates that interval limit, sup indicate The section upper limit；
Step 3 sets and has N to contribute variable the distributed generation resource with correlation in power grid, chooses wherein n-th pair of correlation power output Variable XiAnd XjIt is sampled, establishes the parallelogram model between correlated variables, by parallelogram model conversation at parsing shape The inequality constraints condition of formula:
Wherein ktFor constant, specific value is the slope k of parallelogram model four edges1、k2；
Step 4 enables n=n+1, if n >=N, carries out step 5, otherwise return step 3；
Step 5, with step 2 Chinese style (2), (3), (4), (5) be objective function, step 3 Chinese style (14) be constraint condition to power grid Interval Power Flow is solved；
Step 6, the solution for exporting power grid Interval Power Flow: node voltage amplitude bound, node voltage phase angle bound, branch are active Power bound and branch reactive power bound.
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CN110676860A (en) * 2019-09-04 2020-01-10 武汉大学 Fast prediction unbalance control method based on extended instantaneous active theory
CN112054523A (en) * 2020-10-23 2020-12-08 福州大学 Interval power flow calculation method considering sensitivity classification and correlation
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CN113505468A (en) * 2021-06-08 2021-10-15 西安交通大学 Method for constructing and analyzing interval linear alternating current maximum transmission capacity model
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